Title: Consistent pseudo-maximum likelihood estimators and groups of transformations
Authors: Jean-Michel Zakoian - CREST (France) [presenting]
Christian Gourieroux - University of Toronto and CREST (Canada)
Alain Monfort - ENSAE Paris (France)
Abstract: In a transformation model $y_t = c [a(x_t,\beta), u_t]$, where the errors $u_t$ are i.i.d, the parameters can be estimated by pseudo-maximum likelihood (PML) method, that is by using a misspecified distribution of the errors, but the PML estimator of $\beta$ is in general not consistent. We explain how to nest the initial model in an augmented model with more parameters in order to derive consistent PML estimators of appropriate functions of parameter $\beta$. The usefulness of the consistency result is illustrated by examples of systems of nonlinear equations, conditionally heteroskedastic models, stochastic volatility, or models with spatial interactions.